The turbine rotor of a ship has a mass of 2 tonnes and rotates at \(1800 \mathrm{rpm}\) clockwise when viewed from the left. The radius of gyration of the rotor is \(0.3 \mathrm{~m}\) determine the gyroscopic couple and its effect when

(a) the ship turns at a radius of \(250 \mathrm{~m}\) with speed of \(30 \mathrm{~km} / \mathrm{h}\),

(b) the ship pitches with bow rising at an angular velocity of \(1 \mathrm{rad} / \mathrm{s}\), and

(c) the ship rolls at an angular velocity of \(0.1 \mathrm{rad} / \mathrm{s}\).